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    Instructor: Alexander Stoytchev

    http://www.ece.iastate.edu/~alexs/classes/

    CprE 281: i!ital "o!ic

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    #inary $u%&ers

    CprE 281: Digital Logic 

    Iowa State University, Ames, IA Copyright  Ale!an"er Stoytchev 

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    Ad%inistrative Stu'' 

    (his is the o''icial class we& pa!e:

    http://www.ece.iastate.edu/~alexs/classes/2)1*+Sprin!+281/

    I' you %issed the 'irst lecture, the sylla&us and other class

    %aterials are posted there.

    http://www.ece.iastate.edu/~alexs/classes/2014_Spring_281/ http://www.ece.iastate.edu/~alexs/classes/2014_Spring_281/ http://www.ece.iastate.edu/~alexs/classes/2014_Spring_281/

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    Ad%inistrative Stu'' 

    • -1 is out

    • It is due on ednesday e& 22 0 *p%.

    • Su&%it it on paper &e'ore the start o' the lecture

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    Ad%inistrative Stu'' 

    (he la&s and recitations start next wee:

    •Section : (uesdays, 12:1)  3:))p% 4Coover -all, roo% 2)5)6

    •Section 7: (uesdays, 3:1)  :))p% 4Coover -all, roo% 2)5)6

    •Section 9: ednesdays, 12:1)  3:))p% 4Coover -all, roo% 2)5)6

    •Section : ednesdays, :1)  ;:))p% 4Coover -all, roo% 2)5)6

    •(he la& schedule is posted on the class we& pa!e

     

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    "a&s $ext ee

    Figure 1.5 in the textbook: An FPGA board.

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    "a&s $ext ee

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    Ad%inistrative Stu'' 

    • $o class next >onday 4?niversity -oliday6

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    (he eci%al Syste%

    [https://reader015.{domain}/reader015/html5/0716/5b4bf4a9

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    hat nu%&er syste% is this one@

    [http://freedomhygiene.com/wp-content/themes/branfordmagazine/images/backgrounds/Hands_141756.jpg]

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    (he #inary Syste%

    [ http://divaprojections.blogspot.com/2011/11/alien.html]

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    $u%&er Syste%s

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    $u%&er Syste%s

    n-th digit

    (most significant)

    0-th digit

    (least significant)

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    (he eci%al Syste%

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    (he eci%al Syste%

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    Another ay to "oo at (his

    5 2 4

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    Another ay to "oo at (his

    5 2 4

    102 101 100

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    Another ay to "oo at (his

    5 2 4

    102 101 100

    boxes

    labels

    Each box can contain only one digit and has only one label. From right

    to left, the labels are increasing powers of the base, starting from 0.

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    #ase 

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    #ase 

    base power

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    #ase 

    most significant

    digit

    least significant

    digit

    base power

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    #ase 

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    #inary $u%&ers 4#ase 26

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    #inary $u%&ers 4#ase 26

    most significant bit least significant bit

    base power

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    #inary $u%&ers 4#ase 26

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    Another Exa%ple

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    hat is the value o' this &inary nu%&er@

    •  ) ) 1 ) 1 1 ) )

    • ) ) 1 ) 1 1 ) )

     

    • )B2A   )B2  1B25   )B2*  1B23  1B22  )B21  )B2)

    • )B128  )B*  1B32  )B1  1B8  1B*  )B2  )B1

    • )B128  )B*  1B32  )B1  1B8  1B*  )B2  )B1

    • 32 8  * D ** 4in deci%al6

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    Another ay to "oo at (his

    0 0 1 0 1 1 0 0 2021222324252627

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    So%e (er%inolo!y

    • A &inary di!it is called a bit 

    • A !roup o' ei!ht &its is called a &yte

    • ne &it can represent only two possi&le states,which are denoted with 1 and )

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    Felationship #etween a #yte and a #it

    1 0 1 0 1 1 1 0

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    Felationship #etween a #yte and a #it

    1 0 1 0 1 1 1 0

    1 bit

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    Felationship #etween a #yte and a #it

    1 0 1 0 1 1 1 0

    8 bits = 1 byte

    1 bit

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    #it

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    #it

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    hat is the %axi%u% nu%&er that can &e stored in one &yte 48 &its6@

    hat is the %axi%u% nu%&er that can &e

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    hat is the %axi%u% nu%&er that can &e stored in one &yte 48 &its6@

    •  1 1 1 1 1 1 1 1

    • 1 1 1 1 1 1 1 1

     

    • 1B2A   1B2  1B25   1B2*  1B23  1B22  1B21  1B2)

    • 1B128  1B*  1B32  1B1  1B8  1B*  1B2  1B1

    • 128  *  32  1  8  *  2  1 D 255 4in deci%al6

    • Another way is: 1B28 H 1 D 25 H 1 D 255

    hat would happen i' we try to add 1 to the lar!est

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    hat would happen i' we try to add 1 to the lar!est

    nu%&er that can &e stored in one &yte 48 &its6@

      1 1 1 1 1 1 1 1

     

      1   

      1 ) ) ) ) ) ) ) )

      ) ) ) ) ) ) ) )

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    Analo!y with car odo%eters

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    Analo!y with car odo%eters

    [http://www.hyperocity.com/volvo240/images/Volvo/odometerrepair/speedo999999.jpg]

    eci%al to #inary Conversion

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    eci%al to #inary Conversion

     4?sin! uessin!6

    eci%al to #inary Conversion

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    eci%al to #inary Conversion

     4?sin! uessin!6

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    Convertin! 'ro% eci%al to #inary

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    Convertin! 'ro% eci%al to #inary

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    [ Figure 1.6 in the textbook ]

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    ctal Syste% 4#ase 86

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    #inary to ctal Conversion

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    #inary to ctal Conversion

    1011100101112 = ?8 

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    #inary to ctal Conversion

    1011100101112 = ?8 

    101 110 010 111

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    #inary to ctal Conversion

    1011100101112 = ?8 

    101 110 010 111

     5 6 2 7

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    #inary to ctal Conversion

    1011100101112 = ?8 

    101 110 010 111

     5 6 2 7

    Thus, 1011100101112 =

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    -exadeci%al Syste% 4#ase 16

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    (he 1 -exadeci%al i!its

    ), 1, 2, 3, *, 5, , , 8, ;, A, #, C, , E, 

    1), 11, 12, 13, 1*, 15

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